New Insights into the Actual H-Abstraction Activities of Important Oxygen and Nitrogen Free Radicals: Thermodynamics and Kinetics in Acetonitrile.

The H-abstraction activity of a free radical is a research hotspot and has been extensively studied. In this article, the second-order rate constants of 21 HAT reactions in acetonitrile at 298 K were chosen from several published literature. A kinetic study on the H-abstraction reaction from TEMPOH by a DPPH• radical was carried out. This reaction was researched as an insertion point. By combining this reaction with the 21 HAT reactions in this paper, the thermokinetic parameters of 28 free radicals X and their corresponding antioxidants XH were obtained by the cross-HAT reaction method. The scales of the H-abstraction activities of these 28 oxygen and nitrogen free radicals were determined by using the thermokinetic parameters ΔG ≠o(X). Applications of the thermokinetic parameter ΔG ≠o(X) in assessing the actual H-abstraction activity of a free radical quantitatively and selecting a suitable free radical in scientific research and chemical production were discussed. Predictions of the rate constants by using thermokinetic parameters of reactants were researched, and the reliabilities of the predicted activation free energies of XH/Y reactions were also examined.

Introduction

Free radicals play important roles in many areas of biology and are therefore being actively investigated in connection with various human health problems.[1−4] In recent years, the activities of short-lived N-oxyl radicals such as 4-substituted phthalimide-N-oxyl radicals (4-X-PINO•), 6-substituted benzotriazole-N-oxyl radicals (6-Y-BTNO•), 3-quinazolin-4-one-N-oxyl radicals (QONO•), and 3-benzotriazin-4-one-N-oxyl radicals (BONO•) play key roles in the oxidative degradation of lignin promoted by the laccase/O2 system mediated by NHPI and other hydroxylamines. Hydrogen atom transfers (HATs) from C–H and O–H bonds have been the object of extensive investigation.[5−7] 2,2′,6,6′-Tetramethylpiperidine 1-oxyl (TEMPO•) and its derivatives are popular in radical reactions and academic research studies.[8,9] Alkoxy radicals such as the cumyloxyl radical (CumO•)[10] and tert-butoxyl radical (BuO•),[11] alkyl peroxy radicals (ROO•)[12] such as CumOO• and BuOO•, and phenol radicals (ArO•)[13] are all important oxygen-centered radicals that are involved in a variety of chemical and biological processes. The nitrogen-centered radical 2,2-diphenyl-1-picrylhydrazyl (DPPH•) is a relatively stable neutral radical and is frequently used as a reactive oxygen species (ROS) model to evaluate the radical-scavenging activity of an antioxidant.[14] It has been extensively employed in kinetic studies of H-abstraction from a lot of antioxidants.[15,16] H-abstraction reactions (eq ) are one of the most important reactions of these radicals, and a lot of studies have been devoted to the mechanistic investigations of these processes.

Despite the rapid development of radical chemistry, there is still no one physical parameter that can be used to quantitatively reflect the H-abstraction activity of a free radical in a certain reaction. The H-abstraction activities of different free radicals are usually determined by kinetic tests, which greatly hinder the selection of free radicals in the actual production. In a previous work,[17] a new physical parameter was proposed by a new kinetic model, the thermokinetic parameter ΔG≠o, which can be used not only to directly assess the actual H-abstraction activity of a free radical but also to predict the rate of HAT reaction (eq ) by a kinetic equation (eq ). The two parameters on the right of eq are the thermokinetic parameters of the hydrogen atom donor (XH) and the free radical (Y); the definitions of both parameters are listed in eqs and 4. They can evaluate the actual H-donating activity of a hydrogen atom donor ΔG≠o(XH) and the actual H-accepting activity of a free radical ΔG≠o(Y) accurately and quantitatively. In eqs and 4, ΔGo(XH) is the bond dissociation free energy of the hydrogen atom donor X–H. It is the thermodynamic factor and is usually used to assess the potential H-abstraction capacity of X. ΔG≠XH/X is the activation free energy of self-exchange HAT reaction for XH (XH + X → X + XH). It is the kinetic resistance of the reaction as the thermodynamic driving force is zero, which means the intrinsic kinetic resistance barrier of XH for HAT reaction. It is often called internal resistance energy. The thermokinetic parameter ΔG≠o, which consists of both thermodynamic force and kinetic intrinsic barrier, can be used as the parameter to describe the actual H-donating ability of XH and the H-abstraction ability of X in a chemical reaction during a certain reaction time. According to eqs and 4, the thermokinetic parameter ΔG≠o(X) of X can be determined if the thermokinetic parameter ΔG≠o(XH) and the bond dissociation free energy ΔGo(XH) of XH are known, and vice versa.

To obtain the thermokinetic parameters of free radicals, in this article, three regular kinds of oxygen radicals including the N–O• radical, C–O• radical, and C–O–O• radical and one kind of nitrogen radical, 2,2-diphenyl-1-picrylhydrazyl (DPPH•), were investigated by using the previously proposed kinetic equation (eq ).[18] Parent structures and marks of radicals examined in this work are listed in Scheme .

Scheme 1

Parent Structures and Marks of Radicals Examined in This Work

Results

Determination of the “Thermokinetic Parameter” Values of Free Radicals

Kinetic studies of the HAT reactions from substrates having C–H or O–H bonds of appropriate energies have provided information on the activities of these radicals toward alkylarenes or phenols in the literature.[18−24] At present, the difficulty was to find an appropriate free radical or HAT reaction that could be combined with the HAT reactions in the literature so as to obtain the thermokinetic parameters of the free radicals in Scheme by using eq . After repeated selections, the HAT reaction between TEMPOH and DPPH• (Scheme ) was chosen as the insertion point. The second-order rate constant (k2 = 1.46 × 104 M–1 s–1) of TEMPOH/DPPH• was directly determined using the UV–vis stopped-flow method by monitoring the absorbance decay of DPPH• at 518 nm using the pseudo-first-order kinetic model. The kinetic absorbance decay curve is shown in Figure . The thermodynamic analytical platform for the reaction mechanism of TEMPOH/DPPH• HAT reaction in acetonitrile is analyzed and proved by stoichiometry in the Supporting Information.

Scheme 2

HAT Reaction between TEMPOH and DPPH•

Figure 1

Decay of the 518 nm absorbance of DPPH• (0.10 mM) following the addition of TEMPOH (2.00 mM) in deaerated anhydrous acetonitrile at 298 K (black line) and the fit (red line) using the pseudo-first-order kinetic model.

The activation free energy of the HAT reaction ΔG≠1(H)H/DPPH• is 11.77 kcal/mol, which is obtained by the Eyring equation. As the thermokinetic parameter of DPPH• [ΔG≠o(DPPH•) = −29.67 kcal/mol] has been already available in our previous work,[18] the thermokinetic parameter of TEMPOH, ΔG≠o[1(H)H] = ΔG≠1(H)H/DPPH• – ΔG≠o(DPPH•), can be determined by using eq . The value of ΔG≠o[1(H)H] is 41.44 kcal/mol. As the bond dissociation free energy of TEMPOH, ΔGo[1(H)H] = 65.60 kcal/mol, has been reported in the literature,[25] the activation free energy of self-exchange HAT reaction between 1(H)H and its corresponding radical 1(H), ΔG≠1(H)H/1(H), is 16.37 kcal/mol according to eq . Then, the thermokinetic parameter ΔG≠o[1(H)] of 1(H) can be determined according to eq . The counting process is shown in Scheme .

Scheme 3

Cross-HAT Reaction Method Used for the Determination of Physical Parameters of Radicals in This Work

Then, the cross-HAT reaction method was used to obtain other hydrogen atom donor or radical’s physical parameters by using eqs –4. For example, since the values of k2 for HAT reactions 1(H)H/7 and 1(H)H/11 were reported in refs (19) and (20) (Table , entries 2 and 3), and ΔG≠o[1(H)H] = 41.44 kcal/mol was determined, the thermokinetic parameters of radical 7 ΔG≠o(7) and radical 11 ΔG≠o(11) could be obtained using eq . As the bond dissociation free energies of 7H [ΔGo(7H) = 64.50 kcal/mol][27] and 11H [ΔGo(11H) = 100.73 kcal/mol][26] were reported in the literature, the activation free energies of self-exchange HAT reactions ΔG≠7H/7 and ΔG≠11H/11 were determined according to eq . Then, the thermokinetic parameters ΔG≠o(7H) and ΔG≠o(11H) could be determined according to eq . The counting process is shown in Scheme .

Table 1

Second-Order Rate Constants (k2), Activation Free Energies (ΔG≠XH/Y), and Molar Free Energy Changes (ΔGoXH/Y) of HAT Reactions (XH/Y) in CH3CN at 298 K

entry	XH/Y	k2a (M–1 s–1)	ΔG≠XH/Yb (kcal/mol)	ΔGoXH/Yc (kcal/mol)	ref
1	1(H)H/14	1.46 × 104	11.77	–14.20	this work
2	1(H)H/7	1.90	17.07	1.30	(19)
3	1(H)H/11	5.80 × 106	8.22	–10.63	(20)
4	13H/11	8.70 × 106	7.98	–18.13	(20)
5	1(OCH3)H/14	1.13 × 104	11.92	–15.70	(18)
6	iAscH–/9(OCH3)	5.30 × 105	9.64	–0.22	(21)
	8(G)H/3(H)
7	p-OCH3	5.40 × 106	8.26	–9.90	(22)
8	p-CH3	2.90 × 105	10.00	–6.90	(22)
10	p-H	3.20 × 104	11.30	–5.10	(22)
11	p-Br	2.00 × 104	11.58	–4.60	(22)
	9(G)H/3(H)
12	p-OCH3	1.60 × 105	10.35	–9.80	(22)
13	p-CH3	1.30 × 104	11.84	–7.20	(22)
	9(OCH3)H/3(G)
14	p-CO2CH3	2.00 × 105	10.22	–8.00	(22)
15	p-OCH3	1.30 × 105	10.47	–6.40	(22)
	9(OCH3)H/4(G)
16	p-H	2.20 × 105	10.16	–5.30	(22)
17	p-CF3	7.00 × 105	9.47	–6.70	(22)
18	p-CH3	2.00 × 105	10.22	–5.50	(22)
19	9(OCH3)H/5	1.00 × 106	9.26	–9.20	(22)
20	9(OCH3)H/6	9.40 × 105	9.30	–9.30	(22)
21	TocOH/10	9.40 × 108	5.21	–29.30	(12)
22	TocOH/12	3.80 × 105	9.84	–6.80	(12)

The uncertainty of data is smaller than 5%.

The data of ΔG≠XH/Y are derived from the Eyring equation k2 = (kBT/h) exp(−ΔG≠/RT).

The data of ΔGoXH/Y are derived from the subtraction of the bond dissociation free energies of two substrates: ΔGoXH/Y = ΔGo(XH) – ΔGo(YH).

Using the same method, since the thermokinetic parameters ΔG≠o(XH) of iAscH– [ascorbic acid, ΔG≠o(iAscH–) = 38.11 kcal/mol] and TocOH [tocopherol, ΔG≠o(TocOH) = 43.56 kcal/mol] were obtained in our previous research,[18] and the second-order rate constants of HAT reactions between iAscH–/9(OCH3) and TocOH/10 and TocOH/12 were attainable in refs (15) and (21), the thermokinetic parameters ΔG≠o(X) of radicals 9(OCH3), 10, and 12 could be determined according to eq . As the bond dissociation free energies ΔGo(XH) of 9(OCH3)H, 10H, and 12H were reported in the literature,[21,26] the activation free energies of self-exchange HAT reactions ΔG≠XH/X were determined according to eq . Then, the thermokinetic parameters ΔG≠o(XH) of the corresponding antioxidants could be determined according to eq .

The cross-HAT reactions researched in this article are listed in Table . Except the second-order rate constants k2 and the activation free energies ΔG≠XH/Y of HATs, the Gibbs molar free energy changes ΔGoXH/Y, which were derived from the subtraction of the bond dissociation free energies of two reactants XH and Y, are also listed in Table .

The physical parameters of 28 free radicals are listed in Table . In column 4, the homolytic bond dissociation free energy ΔGo(XH) of X–H and the reference it indexes were listed. In column 5, the activation free energy ΔG≠XH/X of self-exchange HAT reaction for XH (XH + X → X + XH) was listed. The thermokinetic parameter ΔG≠o(XH) of XH and the thermokinetic parameter ΔG≠o(X) of radical X, which respectively could be used to describe the actual H-donating ability of XH and H-abstraction ability of radical X in a chemical reaction during a certain reaction time, were listed in columns 6 and 7.

Table 2

ΔGo(XH), ΔG≠XH/X, ΔG≠o(XH), and ΔG≠o(X) of X in HAT Reaction in CH3CN at 298 K

ΔGo(XH) values are obtained from references.

ΔG≠XH/X values are derived from eqs and 4.

ΔG≠o(XH) = 1/2[ΔG≠XH/X + ΔGo(XH)].

ΔG≠o(X) = 1/2[ΔG≠XH/X – ΔGo(XH)].

ΔG≠o(XH) and ΔG≠o(X) are available in our previous work.[18]

Discussion

Scales of H-Abstraction Activities of Oxygen and Nitrogen Free Radicals

The logical relationship between ΔG≠o(X) and the structures of X is a very important subject. Here, the H-abstraction thermokinetic parameters ΔG≠o(X) of radicals are discussed, as they represent the actual activities of the free radicals to capture the hydrogen atoms in a chemical reaction during a certain reaction time. In Table , the thermokinetic parameters ΔG≠o(X) of 28 radicals are determined. The negative value of ΔG≠o(X) for the radical indicates that the energy is released from the initial state (X) to the transition state (X···H) in HAT reaction.[17,18] According to the physical meaning of ΔG≠o(X) discussed in previous articles,[17,18] the greater the negative value of ΔG≠o(X) is, the stronger the H-abstraction ability of the free radical is. From column 6 in Table , it is clear that the ΔG≠o(X) values of 28 radicals (X) in CH3CN at 298 K range from −23.42 kcal/mol for 4-methoxyl-2,2,6,6-tetramethylpiperidin-1-ol (4-CH3O-TEMPO•) to −41.63 kcal/mol for the cumyloxyl radical (CumO•). Such large ranges of ΔG≠o(X) (−23.42 to −41.63 kcal/mol) indicate that the structures of radicals (X) have a great effect on the ΔG≠o(X) values. To facilitate the application of ΔG≠o(X) values and discover the dependence of ΔG≠o(X) on the structures of radicals (X), the direct-vision dependence of ΔG≠o(X) on the structures of the 28 radicals (X) is shown in Scheme .

Scheme 4

Visual Comparison of ΔG≠o(X) among the 28 Well-Known Free Radicals in Acetonitrile at 298 K

The unit is kcal/mol.

From Scheme , it is clear that the order of H-abstraction activities for these four types of free radicals with different structures is alkoxy radicals (CumO• > BuO•) > short-lived N-oxyl radicals (QONO > BONO > 6-Y-BTNO > 4-X-PINO) > alkyl peroxy radicals (CumOO• > BuOO•) > phenol radicals ≈ DPPH• > TEMPO• derivatives. The structures of X have a great effect on the ΔG≠o(X) values. The ones with the strongest activity of H-abstraction among these free radicals are alkoxy radicals: cumyloxyl radical (CumO•) and BuO•; the values of ΔG≠o(X) are −41.63 and −41.28 kcal/mol, respectively.

Below these two strongest H-abstraction alkoxy radicals, the short-lived N-oxyl radicals show strong H-abstraction activities. Among these four types of short-lived N-oxyl radicals, the activities of H-abstraction are in the order of QONO > BONO > 6-Y-BTNO > 4-X-PINO. For three substituents of 6-Y-BTNO, the activities of H-abstraction are in the order of CF3 > H > CH3, and ΔG≠o(X) values of these three substituted BTNO are very close, which are −36.96 kcal/mol for CF3, −36.26 kcal/mol for H, and −36.22 kcal/mol for CH3. The electronic effect of the substituent has little effect on the actual H-abstraction activity. For three substituents of 4-X-PINO, the activities of H-abstraction are in the order of CO2CH3 > OCH3 > H, and the ΔG≠o(X) values of these three substituted PINO are −36.22 kcal/mol for CO2CH3, −35.96 kcal/mol for OCH3, and −34.94 kcal/mol for H. The order results from both the electronic effect and steric effect. The values of ΔG≠o(X) for QONO and BONO are ΔG≠o(QONO) = −37.17 kcal/mol and ΔG≠o(BONO) = −37.14 kcal/mol, respectively. They are also very close to each other, as these two radicals are similar in chemical structures and bond dissociation free energies.

Below these four short-lived N-oxyl radicals, there are two peroxide radicals, CumOO• and BuOO•. Then, the phenol radicals follow, 4-X-2,6-dimethyl-phenol radicals and 4-X-2,6-di-tert-butylphenol radicals, and the values of ΔG≠o(X) range from 32.42 to 27.54 kcal/mol. For 4-X-2,6-dimethyl-phenol radicals, six substituents are researched and the order of ΔG≠o(X) is Br > H > CH3 > Cl > OCH3 > CN; for 4-X-2,6-di-tert-butylphenol radicals, six substituents are researched and the order of ΔG≠o(X) is CN > Bu ≈ CH3 > OCH3 > H. From these two series, it is not difficult to find that the electronic effect of the substituent does not exactly correspond to the H-abstraction ability of the radical. There are many factors affecting the thermokinetic parameter, including kinetic and thermodynamic factors. In this article, the packing method is used when the thermokinetic parameter ΔG≠o(X) is used to describe the H-abstraction activity of a free radical. The thermokinetic parameter of a free radical, ΔG≠o(X), consists of 1/2ΔG≠XH/X and 1/2ΔGo(XH) according to its definition (eq ). In view of the thermodynamic bond dissociation free energy and the kinetic resistance of a free radical in HAT reaction, ΔG≠o(X) combines these two factors into one parameter to characterize the actual H-abstraction activity of a free radical. Bond polarity, molecular steric hindrance, and other factors are also included in this parameter.

The H-abstraction activity of DPPH• is in the middle of these phenol radicals, and the value of ΔG≠o(DPPH•) is −29.67 kcal/mol. The ones with the weakest activities of H-abstraction among these free radicals are TEMPO• derivatives. TEMPO• derivatives are very stable and are usually used to examine the activities of active antioxidants, such as ascorbate derivatives.[24]

Applications of the Thermokinetic Parameter ΔG≠o(X)

Assessing the Actual H-Abstraction Activities of Free Radicals X

According to the definition of ΔG≠o(X) (eq ), it consists of 1/2ΔG≠XH/X and 1/2ΔGo(XH). As is well known, ΔGo(XH) is the bond dissociation free energy of X–H and is usually used to assess the potential H-abstraction capacity of radical X. The bigger the value of ΔGo(XH) is, the weaker the H-abstraction capacity of the radical is. However, sometimes, the H-abstraction activity of a free radical in a certain reaction is not in accordance with the order of ΔGo(XH). Kinetics need to be taken into account in the actual reaction. For example, the HAT reaction nos. 12 and 17 in Table are listed separately in Table . Two different free radicals 3(H) and 4(CF3) react with the same antioxidant 4-methoxy-2,6-tert-butylphenol 9(OCH3)H. The value of ΔGo[3(H)H] is 3.1 kcal/mol smaller than ΔGo[4(CF3)], indicating that the potential H-abstraction capacity of the radical 3(H) is less than that of the radical 4(CF3). However, the order of second-order rate constants of these two HAT reactions is reversed. It suggests that the H-abstraction activities of free radicals cannot be evaluated solely on the basis of thermodynamic bond dissociation free energies. In Table , we also list another physical parameter of radical X, ΔG≠XH/X, which represents the intrinsic kinetic resistance energy of a radical in HAT reaction. The value of ΔG≠3(H)H/3(H) is 7.14 kcal/mol bigger than ΔG≠4(CF3)H/4(CF3), indicating that the intrinsic resistance barrier of the radical 3(H) in HAT reaction is bigger than that of the radical 4(CF3). Considering the thermodynamic bond dissociation free energy and kinetic resistance, it is easy to find that the H-abstraction activity of a free radical can be much more accurately determined by using the thermokinetic parameter ΔG≠o(X).

Table 3

Comparison of Second-Order Rate Constants of HAT Reactions in Acetonitrile at 298 K

Selection of Suitable Free Radicals

The thermokinetic parameter ΔG≠o(X) can be used not only to compare the H-abstraction activities of different free radicals qualitatively and quantitatively but also to provide data support for the accurate selection of appropriate free radicals in scientific research and chemical production. For example, dihydronicotinamideadenine dinucleotide (NADH) is an extremely important natural redox cofactor, which exists extensively in vivo as an effective hydrogen and electron source to take part in a wide range of biochemical processes.[18] BNAH is usually used as the model of NADH to study its properties. If we want to oxidize BNAH, we can choose suitable free radicals as oxidants according to the thermokinetic parameters of free radicals as long as the thermodynamic feasibility is satisfied. In general, the selection of free radicals should satisfy the following principles: first, the rate constant of HAT reaction is easy to measure (k2’s magnitude is between 10 and 105 M–1 s–1); second, the free radical is stable and has a relatively long lifetime. As ΔGo(BNAH) = 65.80 kcal/mol and ΔG≠o(BNAH) = 44.35 kcal/mol,[18] the value of ΔG≠o(Y) for radicals should be within the scope of −28.27 to −33.72 kcal/mol. The calculation process is provided in the Supporting Information. Considering the rate constant of HAT reaction, two series of phenol free radicals, DPPH•, and two alkyl peroxide radicals can be selected as oxidants for the oxidation of BNAH. Considering the stability and half-life of the free radicals, DPPH• is the most suitable oxidant for the oxidation of BNAH (Scheme ).

Scheme 5

HAT Reaction between BNAH and DPPH•

Predictions of the Rate Constants and Verification of the Predictions

To investigate the reliabilities of thermokinetic parameters for these radicals and the corresponding antioxidants, 35 HAT reactions in the literature[21−23] are selected. According to the values of thermokinetic parameters of the hydrogen atom donors/acceptors in Table , the activation free energies ΔG≠(theor.) of the HAT reactions can be calculated using eq . The activation free energies measured by experiment ΔG≠(exp.) and the difference between these two values [ΔΔG≠ = ΔG≠(theor.) – ΔG≠(exp.)] are listed in Table . The relationships between ΔG≠(theor.) and ΔG≠(exp.) and between ΔΔG≠ and ΔG≠(exp.) are shown in Figure . In Figure a, the black scatterplot is plotted with ΔG≠(exp.) against ΔG≠(theor.), and the line is ΔG≠(theor.) = ΔG≠(exp.). In Figure b, the black scatterplot is plotted with ΔG≠(exp.) against ΔΔG≠, and the red lines on both sides are ΔΔG≠ = −1 kcal/mol and ΔΔG≠ = 1 kcal/mol.

Table 4

Comparison of Theoretical ΔG≠(theor.) Values of HAT Reactions with the Corresponding Experimental Ones ΔG≠(exp.) in Acetonitrile at 298 K

entry	XH/Y	ΔG≠(exp.)a (kcal/mol)	ΔG≠(theor.)b (kcal/mol)	ΔΔG≠c (kcal/mol)	ref
1	1(H)H/9(OCH3)	12.77	12.98	0.21	(21)
	8(G)H/3(CO2CH3)
2	p-OCH3	7.97	8.14	0.17	(22)
3	p-CH3	9.76	9.87	0.11	(22)
4	p-H	11.14	11.18	0.04	(22)
5	p-Br	11.32	11.46	0.14	(22)
	8(G)H/3(OCH3)
6	p-OCH3	8.41	8.40	–0.01	(22)
7	p-CH3	10.25	10.13	–0.12	(22)
8	p-H	11.28	11.43	0.15	(22)
9	p-Br	11.64	11.71	0.07	(22)
	8(G)H/4(H)
10	p-OCH3	9.11	8.10	–1.01	(22)
11	p-CH3	9.69	9.82	0.13	(22)
	8(G)H/4(CF3)
12	p-OCH3	8.15	7.40	–0.75	(22)
13	p-CH3	8.85	9.13	0.28	(22)
14	p-H	10.39	10.44	0.05	(22)
	8(G)H/4(CH3)
15	p-OCH3	9.16	8.14	–1.02	(22)
16	p-CH3	9.82	9.87	0.05	(22)
17	p-Br	12.49	11.46	–1.03	(22)
	8(G)H/5
18	p-OCH3	7.66	7.19	–0.47	(22)
19	p-CH3	8.37	8.92	0.55	(22)
20	p-H	10.43	10.23	–0.20	(22)
21	p-Br	10.73	10.50	–0.23	(22)
	8(G)H/6
22	p-CH3	8.32	8.95	0.63	(22)
23	p-H	10.81	10.26	–0.55	(22)
24	p-Br	11.10	10.54	–0.56	(22)
	8(G)H/14
25	p-CH3	17.78	16.42	–1.36	(23)
	9(G)H/14
26	p-OCH3	17.19	16.77	–0.42	(23)
27	p-CH3	18.86	18.26	–0.60	(23)
	9(CH3)H/3(G)
28	p-OCH3	11.88	11.97	0.09	(22)
29	p-CO2CH3	11.61	11.71	0.10	(22)
	9(CH3)H/4(G)
31	p-H	11.79	11.67	–0.12	(22)
32	p-CF3	11.40	10.97	–0.43	(22)
33	9(CH3)H/5	10.57	10.76	0.19	(22)
	9(G)H/6
34	p-OCH3	7.70	9.30	1.60	(22)
35	p-CH3	10.95	10.79	–0.16	(22)

Derived from experimental measurements.

Derived from ΔG≠o(XH) and ΔG≠o(Y) values in Table according to eq .

ΔΔG≠ = ΔG≠(theor.) – ΔG≠(exp.).

Figure 2

(a) Comparison between the experimentally measured activation free energies of XH/Y and the calculated ones using eq according to the related thermokinetic parameters of XH and Y in Table . (b) ΔΔG≠ = ΔG≠(theor.) – ΔG≠(exp.).

From Figure b, it can be seen that the differences between the experimental values and the predicted values of the activation free energies ΔΔG≠ are quite small. Therefore, the prediction of the rate constants for HAT reactions by using the thermokinetic parameters in eq is highly reliable and accurate. The values of ΔΔG≠ are within ±1.5 kcal/mol and mostly within ±1 kcal/mol. In Figure , the experimental values of reaction activation free energies with large deviations are mainly concentrated in the regions of ΔG≠(exp.) < 8 kcal/mol and ΔG≠(exp.) > 18 kcal/mol. The reaction rates in these regions are too fast or too slow, and the second-order rate constants of the HAT reactions are above the magnitude of 107 M–1 s–1 or below 10–1 M–1 s–1. Therefore, the deviation of the reaction rate may occur in the process of experimental measurement, resulting in a large difference between the experimental value and the predicted value of activation free energy. For example, in Table , the experimentally measured activation free energy of the HAT reaction 9(p-OCH3)H/6 is 7.70 kcal/mol, and the predicted activation free energy is 9.30 kcal/mol. The deviation is 1.60 kcal/mol. The magnitude of the second-order rate constant is 107 M–1 s–1, and the reaction rate of 9(p-OCH3)H/6 is very fast. So, the measurement error of the reaction rate constant may be large, leading to a large ΔΔG≠. ΔG≠(exp.) of reaction 8(p-CH3)H/14 is 17.78 kcal/mol, ΔG≠(theor.) is 16.42 kcal/mol, and ΔΔG≠ is −1.36 kcal/mol. The magnitude of k2 is 10–1 M–1 s–1, and the reaction rate of 8(p-CH3)H/14 is very slow. So, the measurement error of the reaction rate constant may be large, leading to a large ΔΔG≠.

Table 5

Comparison of ΔG≠(exp.) and ΔG≠(theor.) of HAT Reactions in Acetonitrile at 298 K

Another reason for the large ΔΔG≠ is that the kinetic model of eq is based on the classical transition state theory of chemical reaction. The molar free energy change of XH due to the X–H bond dissociation and that of Y due to the Y–H bond formation from Y and H can be described using the Morse-type free energy curves.[18] An approximation is taken in the derivation of eq . That is, the activation free energy of the reaction XH/Y is approximately equal to the sum of the thermokinetic parameters ΔG≠o(XH) and ΔG≠o(Y). The closer the bond dissociation free energies of the two reactants are, the more similar the Morse curves describing the X–H bond dissociation and Y–H bond formation are, and the closer the left and right sides of eq are. Therefore, the large difference between the experimental value and the predicted value of partial HAT reaction’s activation free energies is due to the large difference of bond dissociation free energies between the two reactants and their Morse curves.

Conclusions

In this work, the H-abstraction activities of 28 well-known organic radicals (X) were focused on and researched. The second-order rate constants of 22 HAT reactions from XH to Y in acetonitrile at 298 K were restudied. The thermokinetic parameter values of 28 free radicals and the corresponding antioxidants in acetonitrile at 298 K were determined according to eqs –4. The reliabilities of the predicted activation free energies of XH/Y reactions were also examined. The following conclusions could be drawn:

The thermokinetic parameters ΔG≠o(X) are used to measure the H-abstraction activities of the four types of free radicals with different structures, and the values range from −23.42 kcal/mol for 4-CH3O-TEMPO• to −41.63 kcal/mol for CumO•. The order of H-abstraction activities for these four types of free radicals is alkoxy radicals (CumO• > BuO•) > short-lived N-oxyl radicals (QONO > BONO > 6-Y-BTNO > 4-X-PINO) > alkyl peroxide radicals (CumOO• > BuOO•) > phenol radicals ≈ DPPH• > TEMPO• derivatives. The structures of the radicals (X) have a great effect on the values of ΔG≠o(X).

The prediction of the rate constants for HAT reactions using thermokinetic parameters in eq is highly reliable and accurate. The differences ΔΔG≠ between the experimental and predicted activation free energies are within ±1.5 kcal/mol and mostly within ±1 kcal/mol.

There are two reasons for the large difference ΔΔG≠ between the predicted and experimental activation free energies: one is that the magnitude of the second-order rate constant for the HAT reaction is above 107 M–1 s–1 or below 10–1 M–1 s–1; the other is the large difference of bond dissociation free energies between the two reactants, which results in the large difference of Morse curves between the two reactants.